Despite its continuing assurances that winter home-heating fuel supplies will be adequate, the Department, of Energy yesterday put refiners on notice that it may require them to increase production.

The notice came in the form of rule proposed by DOE's Energy Regulatory Administration, which could force refiners to boost production substantially in the next three months. But energy officials said they do not expelt to have to put the rule into effect.

"If the supply situation is not improved when the heating season begins," an agency announcement said, "extreme hardships could result, especially among comsumers dependent on middle distillates for home heating."

Energy Secretary James R. Schlesinger last week was still assuring the public that heating oil stocks were rising in line with DOE's target, 230 million to 240 million barrels on hand during October.

DOE officials said yesterday that that was still the case and that distillate output last week averaged 3.4 million barrels a day, the highest level of the year.

Despite those encouraging figures, Sen. John Durkin (D-N.H.) complained that DOE's move yesterday was not bold enough to remedy what he described as a "dire situation" in New England.

"This is an encouraging step," durkin said, "but it is too timid . . . the administration could mandate it now, but they are screwing around with this."

Even with higher production of middle distillates -- heating oil, jet and diesel fuel -- in recent weeks, national inventories are still substantially lower than last year's levels.

On July 27, for example, stocks were 164.9 million barrels for all of July last year.

DOE set Aug. 16 as the deadline for public comment on the proposed rule. The department could put it into effect immediately after that, if need be, but DOE officials suggested that would not occur.